In this paper, we show that any L-topological group (G; ¿ ) is uniformizable. That is, we
define, using the family of prefilters which corresponds the L- neighborhood filter at the identity
element of (G; ¿ ), unique left and right invariant L- uniform structures on G compatible with the
L- topology ¿ . On the other hand, on any group G, using a family of prefilters on G fulfills certain
conditions, we construct those left and right L- uniform structures which induce a L- topology ¿
on G for which (G; ¿ ) is an L-topological group and this family of prefilters coincides with the
family of prefilters corresponding to the L- neighborhood filter at the identity element of (G; ¿ ).
Moreover, we show the relation between the L-topological groups and the GTi-spaces, such as:
the L- topology of an L-topological group (resp., a separated L-topological group) is completely
regular (resp., GT31
2
).
Keywords: Fuzzy filters; Fuzzy uniform spaces; Fuzzy topological groups; GTi-spaces; Completely
regular spaces; GT31
2
-spaces; L-Tychonoff spaces. |
